3 Answers
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Methanopyrus kandleri has been able to grow and proliferate at temperatures of up to 122°C when under around 20atm (Takai et. al. 2008). This was achieved in the lab but the theory should hold true for deep sea thermal vents. Another strain of M. kandleri survived incubation to 130°C however was unable to reproduce at this temperature.

One of the key adaptions for thermophiles is the selection towards an extremely thermo-stable copy of the enzyme DNA polymerase. This allows DNA replication at high temperatures and is similar to the 'Taq' polymerase used in the polymer chain reaction in labs, derived from another thermophile, Thermus aquaticus.

I'd add that biochemically speaking, animals and microorganisms from thermal vents tend to have a higher GC content in their genomes, which makes it more thermostable.

All of the proteins are adapted to work at higher temperature. There are a higher number of salt bridges and specific hydrogen bonds in the proteins to stabilize them - more arginines, more glutamic acids, etc. While this reference says that Cysteine is less common, I imagine anything which is not in a reducing environment will have more disulfide bonds - e.g. for proteins on the cell surface.

Sulferous deep sea vents would tend to be reducing as is the inside of the cell, but maybe in the case of fresh hot water spring extemophiles this may be the case.

What about fire? A grass fire across the prairie or a forest fire generates temperatures in excess of those mentioned here and yet many organisms, mostly plants, need fire to allow for seeds to open and germinate. I know fire is a short-lived situation, but is extreme nonetheless. The bark of the burr oak, for example, is rather resistant to fire.